Dumb question: how is this 1.5 inch yearly change out of 239,000 miles measured? Does the measurement assume a perfect spherical Earth?“Lunar distance... is the average distance from the center of Earth to the center of the Moon.
More technically, it is the mean semi-major axis of the geocentric lunar orbit.
It may also refer to the time-averaged distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth–Moon distance.
The lunar distance is approximately a quarter of a million miles.[1]
The mean semi-major axis has a value of 384,402 km (238,856 mi).[2]
The time-averaged distance between Earth and Moon centers is
239,228.3 mi. The actual distance varies over the course of the orbit of the Moon, from 221,500 mi at the perigee to 252,700 mi at apogee, resulting in a differential range of 50,200 km (31,200 mi).[3]
Lunar distance is commonly used to express the distance to near-Earth object encounters.[4]
Lunar distance is also an important astronomical datum; the precision of this measurement to a few parts in a trillion has useful implications for testing gravitational theories such as general relativity,[5] and for refining other astronomical values such as Earth mass,[6] Earth radius,[7] and Earth’s rotation.[8]
The measurement is also useful in characterizing the lunar radius, the mass of the Sun and the distance to the Sun.
Millimeter-precision measurements of the lunar distance are made by measuring the time taken for light to travel between LIDAR stations on the Earth and retroreflectors placed on the Moon.
The Moon is spiraling away from the Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging Experiment.[9][10][11]”
https://en.wikipedia.org/wiki/Lunar_distance_(astronomy)
how is this 1.5 inch yearly change out of 239,000 miles measured? Does the measurement assume a perfect spherical Earth? “The ongoing Lunar Laser Ranging experiment measures the distance between Earth and the Moon using laser ranging.
Lasers on Earth are aimed at retroreflectors planted on the Moon during the Apollo program (11, 14, and 15), the two Lunokhod missions,[1] and the upcoming MoonLIGHT retroreflector to be deployed by the private MX-1E lander.[2][3] The time for the reflected light to return is measured, and the distance is calculated.”
Overview:
The first successful tests were carried out in 1962 when a team from the Massachusetts Institute of Technology succeeded in observing laser pulses reflected from the Moon's surface using a laser with a millisecond pulse length.[4]
Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser.[5]
Greater accuracy was achieved following the installation of a retroreflector array on 21 July 1969, by the crew of Apollo 11, and two more retroreflector arrays left by the Apollo 14 and Apollo 15 missions have also contributed to the experiment.
Successful lunar laser range measurements to the retroreflectors were first reported by the 3.1 m telescope at Lick Observatory, Air Force Cambridge Research Laboratories Lunar Ranging Observatory in Arizona, the Pic du Midi Observatory in France, the Tokyo Astronomical Observatory, and McDonald Observatory in Texas.
The unmanned Soviet Lunokhod 1 and Lunokhod 2 rovers carried smaller arrays. Reflected signals were initially received from Lunokhod 1, but no return signals were detected after 1971 until a team from University of California rediscovered the array in April 2010 using images from NASA's Lunar Reconnaissance Orbiter.[6]
Lunokhod 2's array continues to return signals to Earth.[7] The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions.[8]
The Apollo 15 array is three times the size of the arrays left by the two earlier Apollo missions. Its size made it the target of three-quarters of the sample measurements taken in the first 25 years of the experiment.
Improvements in technology since then have resulted in greater use of the smaller arrays, by sites such as the Côte d'Azur Observatory in Grasse, France; and the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) at the Apache Point Observatory in New Mexico.
Principle:
The distance to the Moon is calculated approximately using this equation:
distance = (speed of light × time taken for light to reflect)/2
In actuality, the round-trip time of about 2.5 seconds is affected by the location of the Moon in the sky, the relative motion of Earth and the Moon, Earth's rotation, lunar libration, weather, polar motion, propagation delay through Earth's atmosphere, the motion of the observing station due to crustal motion and tides, velocity of light in various parts of air and relativistic effects.[9]
Nonetheless, the Earth–Moon distance has been measured with increasing accuracy for more than 35 years. The distance continually changes for a number of reasons, but averages 385,000.6 km (239,228.3 mi).[10]
At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide[11] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (1.9 mi) away. The reflected light is too weak to see with the human eye.
Out of 10^17 photons aimed at the reflector, only one is received back on Earth every few seconds, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic.
This is one of the most precise distance measurements ever made, and is equivalent in accuracy to determining the distance between Los Angeles and New York to 0.25 mm (0.01 in).[8][12]
As of 2002, work is progressing on increasing the accuracy of the Earth–Moon measurements to near millimeter accuracy, though the performance of the reflectors continues to degrade with age.[8]
The upcoming MoonLIGHT reflector, that will be landed in 2019, is designed to increase measurement accuracy 100 times over existing systems.[2][13]
Results:
Lunar laser ranging measurement data is available from the Paris Observatory Lunar Analysis Center,[14] and the active stations. Some of the findings of this long-term experiment are:
The Moon is spiraling away from Earth at a rate of 3.8 cm per year [~1.5 in].[11] This rate has been described as anomalously high.[15]
The Moon probably has a liquid core of about 20% of the Moon's radius.[7]
The universal force of gravity is very stable. The experiments have constrained the change in Newton's gravitational constant G to a factor of (2+/-7)×10−13 per year.[16]
The likelihood of any "Nordtvedt effect" (a differential acceleration of the Moon and Earth towards the Sun caused by their different degrees of compactness) has been ruled out to high precision,[17][18] strongly supporting the validity of the strong equivalence principle.
Einstein's theory of gravity (the general theory of relativity) predicts the Moon's orbit to within the accuracy of the laser ranging measurements.[7]
Gauge freedom plays a major role in a correct physical interpretation of the relativistic effects in the Earth-Moon system observed with LLR technique[19]
https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment
Dumb question: how is this 1.5 inch yearly change out of 239,000 miles measured? Does the measurement assume a perfect spherical Earth? To make it more confusing, don't even think of it that way.
Instead of thinking that the Earth revolves around the Sun and the Moon loops around the Earth, think of them both revolving around the Sun in slightly overlapping orbits.
When the Earth is between the Sun and the Moon, the Earth will be moving slightly faster than the Moon, so the Moon appears to be falling back. When the Moon's gravity pulls on the Earth, it slows the Earth down slightly while pulling the Moon towards it.
The slower Earth now moves slightly farther from the Sun, and the Moon now moves between the Sun and the Earth, making the Moon now move faster than the Earth relative to the Sun.
In effect, it's like a weave where each is revolving around the Sun in slightly oscillating orbits, where sometimes the Earth is closer to the Sun than the Moon, and the other times when the Moon is closer to the Sun than the Earth.
Looking at this article, here are some images that explain the point.
This is what most people think the Moon's orbit is, when referenced only against the Earth.
In reality, when referenced against the Sun, the Moon's orbit looks like this:
Here is a one-month close-up of the Moon's orbit around the Sun:
So, the Moon's orbit is really like a sine-wave around the Sun, sometimes closer and sometimes farther. The Earth's orbit has a much slighter distance movement due to its larger mass, but it moves too. Based on this, it's hard to say that the Moon is flinging away from the Earth, because it would be moving both closer to the Sun and farther from the Sun, not simply wider from the Earth in a loop around it.
-PJ